Abstract: Polished rod load is an important parameter to illustrate the operating potential of sucker rod pumping system. Based on the kinetic characteristic of the pump, the mathematical models of polished rod loads and dynamometer cards are obtained in coalbed methane (CBM) wells. Then the variation of polished rod loads and the string deformation are developed by applying the method. The results show that the computation of polished rod loads should consider the vibration and friction loads. The variation range of polished rod load is large due to the heavy water drainage during the prophase while it is small during the steady flow production. The dynamic and friction to polish rod load ratios are calculated to be 15% and 5%, respectively, which increases the variation range. The static load ratio enhances gradually, and the dynamic load ratio decreases rapidly during the prophase and is just 2.5% during the steady flow production, while the friction load ratio becomes 3.7%. Besides, the total string deformation in CBM wells is just 10% of stroke length, which is much smaller than that in oilfields. And the static deformation is relatively large while the dynamic deformation is small in the total deformation. A mathematical model and dynamometer card for the sucker rod pumping system as the result of this work will provide the reasonable basis for designing and selecting sucker rod pumps.

Key words: Dynamic load, Dynamometer card, Friction force, Polished rod load, Sucker rod pump